| 1 | /* s_tanl.c -- long double version of s_tan.c. |
|---|
| 2 | */ |
|---|
| 3 | |
|---|
| 4 | /* @(#)s_tan.c 5.1 93/09/24 */ |
|---|
| 5 | /* |
|---|
| 6 | * ==================================================== |
|---|
| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
|---|
| 8 | * |
|---|
| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
|---|
| 10 | * Permission to use, copy, modify, and distribute this |
|---|
| 11 | * software is freely granted, provided that this notice |
|---|
| 12 | * is preserved. |
|---|
| 13 | * ==================================================== |
|---|
| 14 | */ |
|---|
| 15 | |
|---|
| 16 | /* tanl(x) |
|---|
| 17 | * Return tangent function of x. |
|---|
| 18 | * |
|---|
| 19 | * kernel function: |
|---|
| 20 | * __kernel_tanl ... tangent function on [-pi/4,pi/4] |
|---|
| 21 | * __ieee754_rem_pio2l ... argument reduction routine |
|---|
| 22 | * |
|---|
| 23 | * Method. |
|---|
| 24 | * Let S,C and T denote the sin, cos and tan respectively on |
|---|
| 25 | * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 |
|---|
| 26 | * in [-pi/4 , +pi/4], and let n = k mod 4. |
|---|
| 27 | * We have |
|---|
| 28 | * |
|---|
| 29 | * n sin(x) cos(x) tan(x) |
|---|
| 30 | * ---------------------------------------------------------- |
|---|
| 31 | * 0 S C T |
|---|
| 32 | * 1 C -S -1/T |
|---|
| 33 | * 2 -S -C T |
|---|
| 34 | * 3 -C S -1/T |
|---|
| 35 | * ---------------------------------------------------------- |
|---|
| 36 | * |
|---|
| 37 | * Special cases: |
|---|
| 38 | * Let trig be any of sin, cos, or tan. |
|---|
| 39 | * trig(+-INF) is NaN, with signals; |
|---|
| 40 | * trig(NaN) is that NaN; |
|---|
| 41 | * |
|---|
| 42 | * Accuracy: |
|---|
| 43 | * TRIG(x) returns trig(x) nearly rounded |
|---|
| 44 | */ |
|---|
| 45 | |
|---|
| 46 | #include <errno.h> |
|---|
| 47 | #include <math.h> |
|---|
| 48 | #include <math_private.h> |
|---|
| 49 | #include <libm-alias-ldouble.h> |
|---|
| 50 | |
|---|
| 51 | _Float128 __tanl(_Float128 x) |
|---|
| 52 | { |
|---|
| 53 | _Float128 y[2],z=0; |
|---|
| 54 | int64_t n, ix; |
|---|
| 55 | |
|---|
| 56 | /* High word of x. */ |
|---|
| 57 | GET_LDOUBLE_MSW64(ix,x); |
|---|
| 58 | |
|---|
| 59 | /* |x| ~< pi/4 */ |
|---|
| 60 | ix &= 0x7fffffffffffffffLL; |
|---|
| 61 | if(ix <= 0x3ffe921fb54442d1LL) return __kernel_tanl(x,z,1); |
|---|
| 62 | |
|---|
| 63 | /* tanl(Inf or NaN) is NaN */ |
|---|
| 64 | else if (ix>=0x7fff000000000000LL) { |
|---|
| 65 | if (ix == 0x7fff000000000000LL) { |
|---|
| 66 | GET_LDOUBLE_LSW64(n,x); |
|---|
| 67 | if (n == 0) |
|---|
| 68 | __set_errno (EDOM); |
|---|
| 69 | } |
|---|
| 70 | return x-x; /* NaN */ |
|---|
| 71 | } |
|---|
| 72 | |
|---|
| 73 | /* argument reduction needed */ |
|---|
| 74 | else { |
|---|
| 75 | n = __ieee754_rem_pio2l(x,y); |
|---|
| 76 | return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even |
|---|
| 77 | -1 -- n odd */ |
|---|
| 78 | } |
|---|
| 79 | } |
|---|
| 80 | libm_alias_ldouble (__tan, tan) |
|---|
| 81 | |
|---|
